Method for generating cam surfaces



April 13, 1965 F. B. BURT 3,

I METHOD FOR GENERATING CAM SURFACES Original Filed Jan. 23, 1957 4Sheets-Sheet l INVENTOR.

FALOW B. Bum.

ATTORNEY April 13, 1965 F. B. BURT 3,177,774

METHOD FOR GENERATING CAM SURFACES Original Filed Jan. 25, 1957 4Sheets-Sheet 2 94 9 we 54 92 Q8 72 I 4 INVENTOR.

FAIELOW B. BURT.

A TTORNE Y.

April 13, 1965 F. B. BURT 3,177,774

METHOD FOR GENERATING CAM SURFACES Original Filed Jan. 23. 1957 4Sheets-Sheet 3 INVENTOR.

FARLOW B. BURT.

MAM

ATTORNEY April 13, 1965 F. B. BURT 3,177,774

METHOD FOR QENERATING CAM SURFACES Original Filed Jan. 23, 1957 4Sheets-Sheet 4 F Cos. X

IN VENTOR.

IE1: E FARLOW B. BURT.

A TTO'QNE United States Patent C) 3,177,774 METHGD FUR GENERATENG CAMSURFACES Farlow B. Burt, Winter Park, Fla, assignor to The Bendix Thepresent invention relates to method for accurately forming cam surfacesof the type having continuously repeating sections spaced about an axisof rotation; and to a particular shape of cam surface which can beaccurately produced very economically by further refinements in thismethod. The present invention is a division of my copending applicationSerial No. 18,113, filed March 28, 1960, now abandoned, which in turn isa division of Patout No. 2,958,264, issued November 1, 1960.

An object of the present invention is the provision of a new andimproved method of forming cam surfaces of the above described type.

Another object of the invention is the provision of a new andimprovedmethod of generating a cam surface in which a rotatable cuttingelement is positioned radially with respect to a blank while the centerof the cutting element and blank are rotated relative to each other toprovide a cylindrical surface of fixed radius, and thereafter thevalleys are formed by relative radial reciprocating movement between thecutting element and blank until the remaining sections of thecylindrical surface are machined to a predetermined length.

Further objects and advantages will become apparent to those skilled inthe art to which the invention relates from the following description:of the preferred embodiments described with reference to theaccompanying drawings forming a part of this specification, in which:

FIGURE 1 is a perspective view of apparatus embodying principles of thepresent invention;

FIGURE 2 is a cross-sectional side view of the apparatus embodyingprinciples of the present invention;

FIGURE 3 is a side view of a cam member finish machined according to thepreferred cam configuration;

FIGURE 4 is a fragmentary side view of a portion of FIGURE 3 betterillustrating a refinement in its contour;

FIGURE 5 is a fragmentary schematic view exaggerating the relationshipbetween the desired cam configuration and cutting element to more fullydepict the principles of the invention; and

FIGURE 6 is a fragmentary schematic view exaggerating the relationshipbetween a preferred form of gearing which strangely enough closelyapproximates a desired corrective phase shifting movement in the aboveapparatus.

There is shown in the drawings apparatus which is specifically designedto machine the cam configuration illustrated in FIGURES 3 and 4 of thedrawings. The cam body member C shown in these views is specificallydesigned for use in sliding vane cam pumps of the type described in theBurt, Sung and Farron Patent No. 2,985,- 110, issued May 23, 1961. Inthis type of pump, a cylindrical rotor member (not shown) is mountedwithin the central opening 10 of the cam, in sliding sealing engagementwith the radially innermost projecting parts or lobes 12 of the cam. Therotor carries a plurality of vanes which are biased radially outwardlyinto engagementwith the cam surface 14, to sweep liquid out of the spacedefined by the valleys, or cam depressions, and the rotor throughsuitable passages in the rotor member. For a more complete descriptionof the construction and operation of the pump for which the cam member Cis de- "ice signed, reference may be had to the above mentionedapplication. r

The specific pump of which cam member C is a part is intended for use inhydraulic power steering systems where substantially pulse free flow isrequired at rotor speeds ranging from 100 to 4000 r.p.m. and atpressures in excess of 1000 p.s.i. Numerous problems are involved indesigning pumps for these conditions. One of these problems is presentedby leakage from a high pressure valley to a low pressure valley throughthe clearance between the separating lobe and rotor; and another ofthese problems is presented by the dynamic forces of the vanes whichtend to separate them from the cam surface. The specific cam contourused in the cam member C is a sinusoidal one conforming to the equationR=r +e cos n6.

, For a moredetailed description of this contour and of the problems ofdesigning pulse free pumps, reference may be had to the above referredto application.

in his work with such pumps, applicant has found that a great reductionin leakage between the cam surface and rotor can be accomplished bymeans of a cylindrical contour in the tip of each lobe without harmfullyatfecting the pulse free operation of the pump. These cylindricalcontours should be confined to the tips of the lobes; and shouldpreferably extend over an arc of from about 2 to about 5 degrees.

The method and apparatus used by applicant to machine the cam contourpreviously described may best be understood by rcference to FIGURE 5 ofthe drawings, where in the pertinent angles and distances are shownexaggerated to better illustrate the relationship involved. The desiredfinished machined contour is generally indicated at 15 and the peripheryof a rotatable cutter of predetermined diameter for machining thecontour is indicated at 16. There is also shown at 18 a line all pointson which are spaced radiallyinwardly from the line 15 towards the center0 of the blank a distance R which corresponds to the radius of thecutter 16. Relatively simple means could be provided for moving thecenter of the rotatable cutter along line 18; but were this to be done,the cutter would not be tangent to the desired contour as seen by thedot-dash line 20, but would dig out too much metal at some spots and notenough at others. In order for the above described cam contour to beable to develop substantially pulse free discharge, the cam contour mustbe machined to an accuracy approaching a few ten thousandths of an inch.This can only be obtained by correcting for the above-stated inaccuracyinvolved in the use of a rotatable cutter.

The applicant has theorized that the above errors could be eliminatedwere means to be provided which, if kept in phase relationship with theangle of rotation of the blank, would move thecenter of the cutter alonga path which is a fixed radial distance from the desired cam contour(i.e. along the line 18); and further has theorized that by suitablychanging the phase relationship between the cutter and the blank, theperiphery of the cutter could be made tangent to the desired contour atall times. A preferred method of accomplishing these results will now beexplained with reference to FIGURE 5 of the drawings. Assume for thetime being that a suitable means is used to provide radial movementbetween the cutter and the blank, and that a further means is providedwhich, when rotated in direct proportion to said first means, moves thecenter. of the cutter along the line 18. Referring to FIG- URE 5, theequation for the desired cam contour 15 will be:

r =r +e cos nqb Where.

r,=radius of any point of the cam defined by angle r ==mean base circlefor the cam e=maximurn variation above and below the base circlen=number of lobes =the angle between any particular radius and anarbitrary reference line through a center of a valley.

For a cutter of radius R, the radius of curve 18 at any +arcrta'n Mgiven point could be r :r R+e cos 11. TaR COS It will be seen that ifthe cutter is moved in and out on Where its radius in phase with itsposition about the cam its center would be at 22 at the angle (1: shownin FIGURE M 005 -1 5. If the center 22 were moved radially inwardly tothe 0 and 1 point 24, the cutter would be tangent to the desired contourat the point T. Point 24 is the distance S from the are (hii w) cener O;and if the cutter were moved out of phase by Sm the angle 0, it wouldhave a radius equal to S. Therefore The above equation expresses themanner in which 0 must to be tangent, the means moving the cutterradially would vary with respect o and Shows the relationship bghave t;have moved an angle proportlonal to when the tween 3 to be quitecomplicated. V cutter ad moved Y "mans of POlar cooldmalesi Appllcantfurther investigated the manner in which a V ra COS nu first cylindricalgear journalled about a point spaced a (1) tan *"Z no distance a fromits center would rotate a similar gear also journalled a distance a fromits center. a The arrangement investigated is seen in FIGURE 6 where thevarious angles (2) S2=ra2+R2 2r R cos (90-41) and distances areappropriately labeled and from which (3) S= R cos (+9) the followingequations are developed:

rewriting 3 2 (7) D =R +a 2aR cos 180P) 1 00s 1; [R Tb+s] D=vR +a +2aRcos P nd R =F +a -2aF cos (180:v)

1 1 F 2 Fcos R =0 =Z arc cos [R-1 +S]-q5 2 a 16+ (a v 2. 2 2 also fromthe law of sines a cos xi (2a 5 x) 401 R S R sin (90- I sin (a) (8) F= acos xix/R a sin a:

\1 V (4) d =aarc sin P= arc SlIl 5 =arc cos Constructing a normal frompoint 24 to the radian F sin a; y yo 1F =arc sin T 2 2 R (bzarc a cosxixR a sln a:)s1n a; a a) 1/R +a +2aR cos P =arc sin (a cosxiw/R a sinx) sing; i /R +a +2aR j;+)

4/ n g Ozarc Sin (a cos wix R a sin 1:) S111 a:

1/R +3a +2a cos x(a cos xix R a? sin m) (99 w) a and x should approach ntimes the theoretical 0 of Sm nation 6 R q By cut and try methodsapplicant was able to establish a-R s -t that, when r =1.25, 12:.375,11:6, 8-023, R-1 for the 00S (90 Tfl b gfiaf, and the a value of thetheoretically desired contour. R A tabulation of data indicating theaccuracy with which h= R cos (9 the 3 Value Provided by the gearingapproaches the theo- R retically required S value for a perfect contouris as fol- (5) tan (Gt-0) lows:

COS Assuming values of a as indicated,

B are sin I S 5111 Eiifitfl 9 I II 0 I II .89570 .0542531 022714 1 1s 43 41 56 89213 .0807788 033955 1 56 45 6 3 15 .88888 .0943158 039790 2 1650 7 43 10 88499 1038389 044000 2 s1 19 9 2s 41 .87823 .1007343 .0468562 41 8 12 1s 52 .87086 .1050154 .045221 2 35 31 15 24 29 86599 .0900484.041781 2 23 39 17 36 21 85941 .0746887 032500 1 52 4 21 7 56 85593.0560054 024537 1 24 21 23 35 39 or input angle :1: output of gearsangle 01 cos :vh=0.23 cos :rS-1.25.375ha gears I I I I 22 11 36 25 3090259 02076 02070 00006 36 19 30 41 25 74902 01725 01713 00012 46 18 052 28 60922 01401 01388 00013 56 52 6 63 55 .43968 01011 00099 00012 7353 t 12 81 4E .1 4263 00328 00328 00005 92 26 5 1 100 33 18300 004210041i 00007 105 38 6 113 10 39501 00900 00901 00008 126 47 36 132 5968179 01568 01559 00000 141 33 54 146 21 83244 01015 01907 00008 It willbe seen that the maximum error is less than 2 ten thousandths of an inchand is therefore acceptable.

Apparatus embodying the above principles is shown in FIGURES 1 and 2 ofthe drawings. The apparatus generally comprises a frame A on which isjournalled a turntable B for supporting and rotating an annular blank Cto be machined. The blank is machined by a rotatable cutter D carried bya high speed electric motor E, which in turn is mounted on a slide Fadapted to be reciprocated so that the cutter moves in a straight linewhich passes through the center of the blank. The slide F is moved backand forth by means of the eccentric G which in turn is rotated by meansof gearing H which provides the proper lead and lag to an in-and-outmovement of the slide to maintain the cutter tangent to the desiredcontour, as discussed above.

The turntable B for supporting and rotating the blank C comprises abottom plate 30, the under surface of which is accurately machined torevolve on a corresponding surface 32 machined into the top face of ahorizontal plate 34 of the frame A. A facing plate 36 recessed in itsupper face to receive the bottom end of the cutter D and to provide chipspace is suitably fastened to the plate and the blank C is adapted to beclamped thereto by the bolts 33. The turntable assembly B is rotated bymeans of a shaft 40 suitably journalled in the frame A; and the bottomend of shaft 40 is coupled to the output shaft 42 of a gear reducer 44having an input shaft 46 adapted to be driven by an electric motor (notshown).

The blank C will usually be rough machined to an internal diameterapproaching the desired distance between opposite lobes of the finishedcam. The rotatable cutting element D adapted to machine the finishedcontour is rotatably supported from the electric motor E which in turnis supported from the slide structure F about to be described. The topplate 43 of the frame is machined parallel to the machine surface 32 toprovide a suitable surface on which the slide structure F reciprocates.Opposite side edges of the slide F are beveled for sliding engagementwith a pair of ways 50 and 52 which in turn are bolted to the top plate48 in a manner assuring that the cutter D will move radially across thecenterline of the turntable B. The electric motor E is supported fromthe slide F by means of blocks 54 and 516, the adjacent ends of whichare suitably recessed to receive opposite sides of the electric motor E;and the electric motor is clamped therebetween by means of the machinebolts 62. The

lock 54 is in turn adjustably positioned upon the slide F by means of aplurality of bolts 64 which extend through slotted holes at in the block5 and are threaded into the slide plate F. Suitable openings and '70 areprovided in the slide plate F and the top plate 413 of the frame,respectively, to receive the electric motor E and permit lateralmovement thereof relative to the blank C.

The slide F is adapted to be reciprocated generally according to adesired sinusoidal function by an eccentric G and a scotch yokestructure 72 fixed to the slide plate F. The scotch yoke structure '72is formed by means of a pair of blocks 74 and '76 adjacent sides ofwhich are suitably recessed to receive opposite sides of a cylindricalrotor 78. The blocks '74 and 76 are confined into tight engagement withopposite sides of the rotor 73 by means of a cross-bar 80 and throughbolts 32 and 84 which extend through openings in opposite side spacermembers 36 and 88 and are threaded into the end of the slide plate F.The spacer members 86 and 08 are of a length which will provide a tightfit between the rotor 78 and the blocks 74 and 76 to overcome lostmotion in the reciprocating structure. The reciprocating cycle of thecutter D may be fed radially outwardly into the blank by means of a handwheel 90 and rod 92 which is threaded into a support block 94 and theend of which is adapted to abut the block 54-. The support block 94 isfixed to slide F by bolts 96; and the end of the rod 92 adjacent thehand wheel 90 is slidably received in an opening 98 in a guide plate 100suitably fixed to the frame A. The block 54 carrying the motor E hasbeen previously described as being adjustably fixed to the slide plate Fby means of slotted holes 66 and bolts 64; and by threading the rod 92inwardly against the block 54, the block 54 may be moved relative to theslide plate F. A dial indicator 102 is shown mounted on the block 54with its sensitive element in engagement with the support block 94 suchthat the depth of cut of the cutter D can be readily determined. As apractical matter, the bolts 64 may be tightened to a point whereinfriction between the block 54 and slide plate F is sufficient to holdthe cutter into cutting engagement with the blank and yet still permitthe block 54 to be moved relative to the slide by means of the threadedrod 92 without further adjustment of the bolts 64-.

The cylindrical rotor 7 3 is mounted eccentrically on the end of a shaft104 by a distance e which in the present instance is equal to 0.023inch. The shaft 104 is suitably journalled in the frame A and is drivenat a rate which is generally six times that at which the blank isrotated to provide a cam having six lobes and six valleys. The shaft 104is driven from a jackshaft 106 by means of gearing H later to bedescribed and the jackshaft 106 is suitably journalled in the frame Aand driven at a rate six times that of the shaft40 by means of gears 108and 110 fixed to the shafts 40 and 106 respectively.

The gear means H is adapted to provide the correction by means of whichthe cutter element D is maintained tangent to the desired cam contour,utilizing the principles previously described with reference to FIGURE 6of the drawing. The gear means H comprises two cylindrical gears eachhaving a pitch diameter of two inches and each of which is mounted onits respective shaft eccentrically by a distance a, which in the presentinstance is equal to 0.106 inch. The gear 112 which is fixed to theshaft res will correspond generally to the left-r and gear depictedinFIGURE 6; and the gear 114 fixed to the shaft 104 will correspond tothat shown in the righthand side of the same figure.

In the preferred method of operating the apparatus above described, agear blank C finished to a rough in ternal diameter will be bolted tothe turntable B. The cutter D will be positioned within the opening ofthe blank C, and the gear 112 will be removed from the shaft 104 so thatthe slide F will not be reciprocated relative to the blank. The handwheel 90 will be turned to gradually advance the rotating cutter Dradially into the blank C until its internal diameter corresponds to thedesired distance between the cylindrical surfaces 116 in opposite lobesof the finished cam. Once this diameter has been accurately machined thegear 112 is inserted upon the shaft 104 and the eccentric means Gsuitably rotated to provide reciprocatory movement of slide structureF.Prior to the time that the slide structure F is reciprocated relative tothe blank, the motor B will be moved radially inwardly a sufiicientdistance such thatthe cutter D will not engage the surfaces of the blankabout to be machined when the reciprocation of the slide structure isstarted. Thereafter the rod 92 is threaded inwardly until thereciprocatory cycle is moved outwardly to a point where the cutter Dbegins to engage the blank during the radially outermost portion of itscycle. E11- gagement of the cutter D during its outermost extremity ofradial movement begins to form the valleys in the blank C; and bygradually advancing the rod 32 into the support member 94, these valleyswill be deepened until all that remains of the original cylindricalinternal surface are the sections which are to be left in the tips ofeach of the lobes. These cylindrical surfaces 116 will preferably befrom 2 to 5 degrees in length. It will be seen that the chordal lengthof the cylindrical surfaces 116 will be gradually reduced as themachining of the cam progresses. The cylindrical surfaces 116 provide amark which can readily be seen by the operator; and when this mark hasdecreased to approximately 50 or 60 thousandths of an inch (which can bejudged by eye,

by a skilled machinist) the machining of the cam is com- By this simpleexpedient the sinusoidal surfaces The apparatus shown in the drawingscan be used to machine external cams as well as internal cams; and bysuitably alternating the eccentric G and gearing H the same principlescan be used to form cams having a configuration other than thesinusoidal one of the cam shown in FIG- URE 3.

While the invention has been described in considerable detail, I do notwish to be limited to the particular methods and constructions shown anddescribed, and it is my intention to cover hereby all novel adaptations,modifications and arrangements thereof which come within the practice ofthose skilled in the art to which the invention relates.

I claim:

1. The method of machining the fluid pressure chamber forming cam memberof a vane type positive displacement fluid handling device, comprising:moving a rotating cutting element radially with respect to a rotatingblank until a cylindrical surface of said predetermined diameter isformed; thereafter reciprocating said rotating cutting element radiallywith respect to said rotating blank according to a predetermined cycle;and gradually advancing said reciprocating cycle of said cutting elementradially with respect to said cylindrical surface to gradually removemore and more metal until the remaining cylindrical surfaces are of apredetermined length.

2. The method of machining the fluid pressure chamber forming cam memberof a vane type positive displacement fluid handling device in a machinehaving.

means for supporting a blank, means for supporting a rotatable cutter,means for producing relative rotation between the blank and cutter, andmeans for moving the blank and cutter radially relative to each other,said method comprising: mounting the blank in the machine; providingrelative rotation between the blank and the center of the cutter;gradually moving the cutter and blank radially relative to each otheruntil a cylindrical surface of predetermined diameter is generated;moving the cutter and blank radially relative to each other to anoncutting position; providing a relative radially reciprocatingmovement between the blank and cutter in predetermined phaserelationship to relative rotational movement between the blank andcutter; and gradually advancing the radially reciprocating movementbetween the cutter and blank into the cylindrical surface of the blankuntil the remaining portions of the cylindrical surface are of apredetermined length.

3. The method of machining the fluid pressure chamber forming cam memberof a vane type positive displacement fluid handling device in a machinehaving means for supporting a blank, means for supporting and rotating arotatable cutter, means for moving the blank radially with respect tothe cutter, and means for moving the blank and cutter radially relativeto each other, said method comprising: mounting the blank in themachine; gradually moving the cutter and blank radially into therotating blank until a cylindrical surface of predetermined diameter isgenerated; moving the cutter radially out of cutting engagement withrespect to the blank; providing a cyclic radially reciprocating movementto the cutter in predetermined phase relationship to the rotation of theblank; and gradually advancing theeycle of the cutter into thecylindrical surface of the blank until the remaining portions of thecylindrical surface are of a predetermined length.

References Cited by the Examiner UNITED STATES PATENTS 1,833,003 12/31Hill -3 2,917,693 12/59 Cail.

WILLIAM W. DYER, 111., Primary Examiner.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION Patent No. 3 ,177,774 April 13, 1965 Parlow B. Burt It is hereby certified that errorappears in the above numbered patent requiring correction and that. thesaid Letters Patent should read as corrected below.

Column 3, line 57, the equation should appear as shown below instead ofas in the patent:

line '61, the equation should appear as shown below instead of as in thepatent:

R sin [90-41) tan (on 4)) r -R cos (90w) Signed and sealed this 12th dayof October 19656 (SEAL) Attest:

ERNEST W. SWIDER EDWARD J, BRENNER Attesting Officer Commissioner ofPatents

1. THE METHOD OF MACHINING THE FLUID PRESSURE CHAMBER FORMING CAM MEMBEROF A VANE TYPE POSITIVE DISPLACEMENT FLUID HANDLING DEVICE, COMPRISING:A MOVING A ROTATING CUTTING ELEMENT RADIALLY WITH RESPECT TO A ROTATINGBLANK UNTIL A CYLINDRICAL SURFACE OF SAID PREDETERMINED DIAMETER ISFORMED; THEREAFTER RECIPROCATING SAID ROTATING CUTTING ELEMENT RADIALLYWITH RESPECT TO SAID ROTATING BLANK ACCORDING TO A PREDETERMINED CYCLES;AND GRADUALLY ADVANCING SAID RECIPROCATING CYCLE OF SAID CUTTING ELEMENTRADIALLY WITH RESPECT TO SAID CYLINDRICAL SUR-